Institut für Theoretische Physik

Articles

• M. Ruggenthaler, G. Grübl, S. Kreidl, Times of arrival: Bohm beats Kijowski, Journal of Physics A. Mathematical and General 38, 8445-8451 (2005) URL Alternative URL (local copy) Preprint Identifier;  doi:10.1088/0305-4470/38/39/010;

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  We prove that the Bohmian arrival time of the one-dimensional Schrödinger evolution violates the quadratic form structure on which Kijowski's axiomatic treatment of arrival times is based. Within Kijowski's framework, for a free right moving wave packet Ψ, the various notions of arrival time (at a fixed point x on the real line) all yield the same average arrival time t_Kij(Ψ) . We derive the inequality t_B(Ψ) ≤ t_Kij(Ψ) relating the average Bohmian arrival time to that of Kijowksi. We prove that t_B(Ψ) < t_Kij(Ψ) if and only if Ψ leads to position probability backflow through x .
   

Proceedings

• G. Grübl, S. Kreidl, M. Penz, M. Ruggenthaler, Arrival time and backflow effect, QUANTUM MECHANICS: Are There Quantum Jumps? - and On the Present Status of Quantum Mechanics (Trieste (Italy) and Losinj (Croatia), 7-9 September 2005), AIP Conference Proceedings 844, 177-191 (2005) URL; doi:10.1063/1.2219361.

Articles

• G. Grübl, The quantum measurement problem enhanced, Physics Letters A 316 3-4, 153-158 (2003) URL Alternative URL (local copy) Preprint Identifier; doi:10.1016/S0375-9601(03)01098-3.

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  The quantum measurement problem as formalised by Bassi and Ghirardi [Phys. Lett. A 275 (2000) 373] without taking recourse to sharp apparatus observables is extended to cover impure initial states.
• S. Kreidl, G. Grübl, H. G. Embacher, Bohmian arrival time without trajectories, Journal of Physics A. Mathematical and General 36, 8851-8865 (2003) URL Alternative URL (local copy) Preprint Identifier; doi:10.1088/0305-4470/36/33/309.

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  The computation of detection probabilities and arrival time distributions within Bohmian mechanics in general needs the explicit knowledge of a relevant sample of trajectories. Here it is shown how for one-dimensional systems and rigid inertial detectors these quantities can be computed without calculating any trajectories. An expression in terms of the wavefunction Ψ and its spatial derivative ∂_x Ψ, both restricted to the boundary of the detector's spacetime volume, is derived for the general case, where the probability current at the detector's boundary may vary its sign.

Articles

• G. Grübl, K. Rheinberger, Time of arrival from Bohmian flow, Journal of Physics A. Mathematical and General 35, 2907-2924 (2002) URL Alternative URL (local copy); doi:10.1088/0305-4470/35/12/313.

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  We develop a new conception for the quantum mechanical arrival time distribution from the perspective of Bohmian mechanics. A detection probability for detectors sensitive to quite arbitrary spacetime domains is formulated. Basic positivity and monotonicity properties are established. We show that our detection probability improves and generalizes an earlier proposal by Leavens and McKinnon. The difference between the two notions is illustrated through application to a free wavepacket.

Articles

• G. Grübl, R. Moser, K. Rheinberger, Bohmian trajectories and Klein’s paradox, Journal of Physics A. Mathematical and General 34, 2753-2764 (2001) URL Alternative URL (local copy); doi:10.1088/0305-4470/34/13/307.

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  We compute the Bohmian trajectories of the incoming scattering plane waves for Klein’s potential step in explicit form. For finite norm incoming scattering solutions we derive their asymptotic space-time localization and we compute some Bohmian trajectories numerically. The paradox, which appears in the traditional treatments of the problem based on the outgoing scattering asymptotics, is absent.

Articles

• P. Horak, G. Grübl, Pair creation in the adiabatic limit: a solvable example, Journal of Physics A. Mathematical and General 28, 223-230 (1995) URL Alternative URL (local copy); doi:10.1088/0305-4470/28/1/024.

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  A strictly positive lower bound is derived for the average number of chiral fermion/antifermion pairs which are created from the two-dimensional Minkowski space vacuum by an infinitely differentiable external potential of compact support in the adiabatic limit.

Articles

• G. Grübl, C. Reitberger, Fermion number creation via electromagnetism, Letters in Mathematical Physics 26 4, 235-243 (1992)  Alternative URL (local copy); doi:10.1007/BF00420232.

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  Let an external current, whose support is confined to the space-like slab |x⁰| < T in two-dimensional spacetime, build up a localized charge density which vanishes for times |x⁰| > T. We show that the zero mass Dirac quantum field reacts to this current by a c-number shift of the fermion number, i.e. Q_out = Q_in + ΔQ, with ΔQ = ∫_-∞^∞ dx⁰ ∫_-∞^x0 dξ q(ξ )/π , where q(x⁰) denotes the total external charge. For the shift of the axial charge we obtain an extension of existing results.
• H. G. Embacher, G. Grübl, M. Oberguggenberger, Products of Distributions in Several Variables and Applications to Zero-Mass QED_2, Journal for Analysis and its Applications 11, 437-454 (1992)  Alternative URL (local copy)

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  We study products of distributions in serveral variables, having in mind applications to quantum electrodynamics. We introduce a new product, the parameter product, and relate it to known ones. It allows us to rigorously interpret and evaluate products arising in the computations of the one-loop vacuum polarization of zero-mass QED₂ , thereby avoiding the occurrence of renormalization ambiguities from the very beginning.
• G. Grübl, R. Vogl, Boost action on external field problems, Journal of Physics A. Mathematical and General 25, 2737-2744 (1992) URL Alternative URL (local copy); doi:10.1088/0305-4470/25/9/040.

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  The authors study the behaviour of chiral fermions in two-dimensional space-time with an external potential under the action of Lorentz boosts. Quantization of the system such that the incoming field is in the physical vacuum representation of the fermionic field algebra associated with the canonical anticommutation relations algebra, makes time evolution and boosts unitarily implemented at all times. The models are shown to possess an instantaneous particle interpretation in exceptional cases only. In the cases they do, in general this property is destroyed by boosts. Thus boost invariance of instantaneous vacua, as has been conjectured recently, can be ruled out.
• G. Grübl, R. Vogl, Unitary time evolution for irregular external field problems, Helvetica Physica Acta 65, 53-55 (1992) Alternative URL (local copy).

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  For second quantized fermionic systems with static first quantized hamiltonian we proof that existence of a Schrödinger picture is not equivalent to the condition defining the regular external field problem.

Articles

• H. G. Embacher, G. Grübl, Fourier representation for the two-point function of the two-dimensional massless scalar field, Letters in Mathematical Physics 22 3, 235-238 (1991) Alternative URL (local copy); doi:10.1007/BF00403550.

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  The Fourier transform of the (indefinite metric) Wightman two-point function - (1/4π) ln( - x² + i ε x⁰ ) |_{ε↓0} of a free massless scalar quantum field in two-dimensional spacetime has been inconsistently reported by various authors. We compute the correct one from the definition of the Fourier transform of tempered distributions.

Articles

• M. Ritter, F. Lang, G. Grübl, H. G. Embacher, Determination of cell membrane resistance in cultured renal epithelioid (MDCK) cells. effects of cadmium and mercury ions, Pflügers Archiv European Journal of Physiology 417 1, 29-36 (1990)  Alternative URL (local copy); doi:10.1007/BF00370765.

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  Previous studies have indicated that the cell membrane of Madin Darby Canine Kidney (MDCK) cells is hyperpolarized by a number of hormones and trace elements, in parallel with an enhancement of potassium selectivity. Without knowledge of the cell membrane resistance (R_m), however, any translation of potassium selectivity into potassium conductance remains equivocal. The present study was performed to determine the R_m of MDCK cells by cellular cable analysis. To this end, three microelectrodes were impaled into three different cells of a cell cluster; current was injected via one microelectrode and the corresponding voltage deflections measured by the other two microelectrodes. In order to extract the required specific resistances, the experimental data were analysed mathematically in terms of an electrodynamical model derived from Maxwell's equations. As a result, a mean R_m of 2.0±0.2 kΩcm² and an intercellular coupling resistance (R_c) of 6.1±0.8 MΩ were obtained at a mean potential difference across the cell membrane of -47.0±0.6 mV. An increase of the extracellular K⁺ concentration from 5.4 to 20 mmol/l depolarized the cell membrane by 16.2±0.5 mV and decreased R_m by 30.6±3.0%; 1 mmol/l barium depolarized the cell membrane by 20.1±1.1 mV and increased R_m by 75.9±14.3%. Omission of extracellular bicarbonate and carbon dioxide at constant extracellular pH caused a transient hyperpolarization (up to –60.4±1.4 mV), a decrease of R_m (by 75±4.5%) and a decrease of R_c (by 23.1±8.4%). The changes in R_m and R_c were probably the result of intracellular alkalosis. Cadmium ions (1 μmol/l) led to a sustained, reversible hyperpolarization (to –64.8±1.3 mV) and to a decrease of R_m (by 77.0±2.7%); mercury ions (1 μmol/l) cause a sustained hyperpolarization (to –60.1±1.2 mV) and a decrease of R_m (by 76.3±3.9%). Neither manoeuvre significantly altered R_c. We have previously shown that both cadmium and mercury hyperpolarize the cell membrane potential and increase its potassium selectivity; the decrease of the R_m observed in the present study indicates that these effects are due to an increase of the potassium-selective conductance of the cell membrane.

Articles

• G. Grübl, Dynamical squeezing in quantum mechanics, Journal of Physics A. Mathematical and General 22, 3243-3252 (1989) URL Alternative URL (local copy); doi:10.1088/0305-4470/22/16/015.

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  The time evolution orbits of Gaussian vectors under a harmonic oscillator dynamics are computed and discussed. The generic case is shown to be this: a minimum uncertainty vector which is coherent with respect to a harmonic oscillator Hamiltonian with smaller frequency than the one of the driving Hamiltonian, evolves into a minimum uncertainty vector with reduced position variance for exactly two discrete instants of time per period. The results are applied to the case of a perturbing frequency jump in the driving harmonic oscillator Hamiltonian. The total transition probability to the excited (unperturbed) oscillator levels from the ground-state vector is computed.

Articles

• H. G. Embacher, G. Grübl, Axial anomaly and Schwinger terms in two-dimensional general quantum field theory, Physical Review D (Particles and Fields) 38 2, 597-597 (1988) URL Alternative URL (local copy); doi:10.1103/PhysRevD.38.597.

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  We compute the vacuum expectation value (Ω, j^μ(x) j^ν(y) Ω) ≡ J^μν(x-y) for a relativistic, Hermitian, not necessarily local vector field in two-dimensional space-time when ∂_μ J^μν = ∂_μ J^νμ = ∂_μ ε_α^μ J^αν = ∂_μ ε_α^μ J^να = 0 holds in S’(R²), the space of tempered distributions. As the space-time symmetry group of the model we take the inhomogeneous proper orthochronous Lorentz group P₊^↑. (Ω, Tj^μ (x) j^ν (y) Ω) is verified to have anomalous (axial-)vector Ward identities due to nonvanishing equal-time current-current commutators. Additional conditions on j^μ are specified which imply that j^μ is a free zero-mass Wightman field with ∂_μ j^μ = ∂_μ ε_ν^μ j^ν = 0.
• H. G. Embacher, G. Grübl, R. Patek, Explicit Soliton Solution to the Bosonized Jackiw-Rebbi Model with Fermion Number 1/2, Europhysics Letters 5, 497-501 (1988) Alternative URL (local copy).

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  We study the half-integer charged-soliton sector of the (φ)⁴ Higgs-type scalar field model with Yukawa coupling to a massless Dirac field in 2-dimensional space-time in its bozonized version: we find the one-soliton solution to the coupled nonlinear field equations of the model which represents the quantum soliton with fermion number 1/2 and compute its mass. A comparison with the corresponding c-number solution of the fermionic model is included.

Articles

• H. G. Embacher, G. Grübl, R. Patek, Gauge-invariant energy-momentum tensor for massive QED, Physical Review D (Particles and Fields) 33, 1162-1165 (1986) URL Alternative URL (local copy); doi:10.1103/PhysRevD.33.1162.

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  For massive QED with a gauge-fixing term a candidate for the energy-momentum tensor is presented. Both cases of scalar and spinor matter fields are treated. The energy-momentum tensor is invariant under the restricted gauge transformations which exist in that model. This property guarantees that the unphysical scalar photons do not contribute to the energy-momentum densities. The difference between the translational generators and the energy-momentum observables is pointed out.

Articles

• C. Leubner, G. Grübl, Interrelation of Euler’s and Piña’s parametrizations of rotations, American Journal of Physics 53, 487-488 (1985) ; doi:10.1119/1.14208

Articles

• A. Z. Capri, G. Grübl, R. Kobes, Fock space construction of the massless dipole field, Annals of Physics 147 1, 140-170 (1983) URL Alternative URL (local copy); doi:10.1016/0003-4916(83)90069-6.

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  We construct the Fock space representation of the free massless scalar dipole field in terms of creation and annihilation operators for the eigenvectors of the momentum operator. The Poincare group is implemented unitarily only on a subspace of the full (positive metric) Hilbert space. The subspace possesses a hermitean, local, irreducible scalar field constructed out of the (non-hermitean) dipole field. Thus this subspace is a perfect candidate for a physical subspace of observable particles. We show that this possibility is however excluded by the fact that these particles interact with an external c-number source in a manner that violates unitarity. We illustrate our construction by applying it to the linearized Higgs model with external c-number source and examine the (non-trivial) dynamics of the dipole degrees of freedom in this case. An explicit separation of the physical degrees of freedom from the unphysical ones is presented for this interacting model.
• A. Z. Capri, G. Grübl, R. Kobes, A quantization of the electromagnetic field, Canadian Journal of Physics 61, 1172-1183 (1983) Alternative URL (local copy).

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  Quantization of the electromagnetic field in a class of covariant gauges is performed on a positive metric Hilbert space. Although losing manifest covariance, we find at the free field level the existence of two physical spaces where Poincaré transformations are implemented unitarily. This gives rise to two different physical interpretations of the theory. Unitarity of the S operator for an interaction with an external source then forces one to postulate that a restricted gauge invariance must hold. This singles out one interpretation, the one where two transverse photons are physical.

Articles

• G. Grübl, A. Z. Capri, Consistency check for asymptotic convergence of classical Yang-Mills fields in the Lorentz gauge, Physical Review D (Particles and Fields) 26, 1408-1414 (1982) URL Alternative URL (local copy); doi:10.1103/PhysRevD.26.1408.

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  We derive the class of restricted local gauge transformations of Yang-Mills fields that leave the four-divergence of these fields invariant. They form a symmetry of the Yang-Mills equations combined with the Lorentz condition and lead, in Euclidean space-time, to the Gribov ambiguity. We make use of this symmetry in order to check possible inconsistencies arising from the supposition of asymptotic convergence of classical Yang-Mills fields, obeying the Lorentz condition, to free fields. Inconsistencies would support the common conjecture of color confinement. We show that residual gauge transformations of the interpolating fields induce Abelian gauge transformations and global SU_n rotations on the hypothetical asymptotic fields thereby revealing no inconsistency of the hypothetical asymptotic convergence.

Articles

• G. Grübl, A Generalization of the Higgs Model without Dipole Ghosts, Nuovo Cimento A 59, 433-446 (1980) Alternative URL (local copy).

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  The Abelian Higgs model displays unorthodox features such as nonunitary translation operators and dipole singularities in the propagators of the Goldstone and the vector field. In order to circumvent mathematical difficulties due to these singularities, the Higgs model is here generalized by the inclusion of a mass term in the free Lagrangian of the vector field. This model is first systematically discussed on the classical level, including the construction of a positive-definite energy density and the formulation of the classical counterpart to spontaneous symmetry breaking. Then the Fock-space representation is given for the linearized model, which is shown to possess unitary translation operators and to be free of dipole singularities. The propagator of the vector field is demonstrated to be well behaved in the ultraviolet limit. Four kinds of particles are shown to occur in the theory: vector, Goldstone, Higgs and gauge particles.The coupling between them is studied by simulation of the interaction through external sources. It turns out that the massive gauge particles always decouple from the other particles, which guarantees that they are unobservable. The coupling of the Goldstone particles is governed by the mass parameter of the vector field and vanishes only in the zero limit of this parameter.
• G. Grübl, C. Leubner, Current misconception concerning the time evolution operator, American Journal of Physics 48, 484-485 (1980); doi:10.1119/1.12314

Dissertation

• G. Grübl, Mesontheorie der elastischen Nukleon-Antinukleon-Streuung bei niedrigen Energien (1980)

Diploma Thesis

• G. Grübl, Zur Lichtablenkung in einer linearen Gravitationstheorie (1977)